Rayleigh Distribution Calculator

About this calculator

The Rayleigh distribution describes the magnitude of a 2D vector whose components are independent, zero-mean, equally-scaled normal random variables. Its probability density function is f(x) = (x/σ²) × e^(−x²/2σ²) and its cumulative distribution function is F(x) = 1 − e^(−x²/2σ²), with mean = σ√(π/2), variance = (4−π)/2 × σ², and mode = σ.

Wireless communications engineers use it to model signal amplitude fading in environments with many scattered, reflected signal paths and no dominant line-of-sight (Rayleigh fading), meteorologists use it to model wind speed distributions, and reliability engineers use it for failure-time analysis when a failure rate increases linearly with time.